15 citations · 42 across the 11 of their papers we have counts for
12 papers · 1 filter
Rotational Weingarten surfaces in Lorentz-Minkowski space
Paula Carretero, Ildefonso Castro, Ildefonso Castro-Infantes
We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect…
surfaces in hyperbolic and de Sitter spaces with Cantor ends
Ildefonso Castro-Infantes, Jorge Hidalgo
We prove that on every compact Riemann surface there is a Cantor set such that admits a proper conformal constant mean curvature one ($\mathrm{CMC…
Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure
Antonio Alarcon, Ildefonso Castro-Infantes, Jorge Hidalgo
We prove that every open Riemann surface is the complex structure of a complete surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space $\mathbb{H}^3…
Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous fun…
Spherical curves whose curvature depends on distance to a great circle
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
Motivated by a problem posed by David A. Singer in 1999 and by the elastic spherical curves, we study the spherical curves whose curvature is expressed in terms of the distance to…
Erratum to "Interpolation and optimal hitting for complete minimal surfaces with finite total curvature"
Antonio Alarcon, Ildefonso Castro-Infantes, Francisco J. Lopez
We correct a mistake in the paper with the mentioned title and reference: Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:21. It corresponds with the preprint arXiv:…
Interpolation by complete minimal surfaces whose Gauss map misses two points
Ildefonso Castro-Infantes
Let be an open Riemann surface and let be a closed discrete subset. In this paper, we prove the existence of complete conformal minimal immersions $M\to\mathbb{R}^…
Carleman approximation by conformal minimal immersions and directed holomorphic curves
Ildefonso Castro-Infantes, Brett Chenoweth
Let be an open Riemann surface. In this paper we prove that every continuous function , , defined on a divergent Jordan arc $M \subset \ma…
Curves in Lorentz-Minkowski plane with curvature depending on their position
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propou…
Interpolation and optimal hitting for complete minimal surfaces with finite total curvature
Antonio Alarcon, Ildefonso Castro-Infantes, Francisco J. Lopez
We prove that, given a compact Riemann surface and disjoint finite sets and , every map extends to a complete conform…
Interpolation by conformal minimal surfaces and directed holomorphic curves
Antonio Alarcon, Ildefonso Castro-Infantes
Let be an open Riemann surface and be an integer. We prove that on any closed discrete subset of one can prescribe the values of a conformal minimal immersion $M\t…
Complete minimal surfaces densely lying in arbitrary domains of
Antonio Alarcon, Ildefonso Castro-Infantes
In this paper we prove that, given an open Riemann surface and an integer , the set of complete conformal minimal immersions with $\overline{X(M)}=\m…